Known controlling systems for dynamic systems used in technology are either designed purely conventionally on the basis of linear or nonlinear system models, or consist of pure fuzzy control controllers. Each of the two fundamentally dissimilar approaches has its own typical advantages and disadvantages in this regard. The so-called sliding mode controllers with boundary layer stand particularly from among the conventional controlling systems, since these most readily do justice to the requirements for robustness and the involvement of a minimum of system knowledge (J. F. Slotine: The Robust Control of Robot Manipulation; The Intern. Journ. of Robotics Research (MIT), Vol. 4, No. 2, 1985, pages 49-64). These controllers are conventional controllers for higher-order (n&gt;=2) systems, which have a compensation component for system nonlinearities and a boundary layer around the sliding surface (SS), in order to achieve a continuous%change in sign of the manipulated variable. A precondition for designing a controller of this type is to how the upper limits of the model uncertainties, parameter fluctuations, disturbances and frequencies which occur. A disadvantage of this controller is that a relatively deep knowledge of the nonlinear system components is a precondition for designing the compensation component, and this greatly restricts the variability of a controller of this type once it has been set.
An alternative to conventional control principles is provided by the fuzzy controllers, which are frequently designed on the basis of a two-dimensional phase plane (Mamdani. E. H. and Assilian S.; Art Experiment in Linguistic Synthesis with a Fuzzy Logic Controller; In: E. H. Mamdani & B. R. Gaines, Fuzzy Reasoning and its Applications, London, Academic Press, 1981, pages 311-323). These operate in principle like sliding-mode controllers with a boundary layer (S. Kawaji, N. Matsunaga: Fuzzy Control of VSS Type and its Robustness; IFSA 91, Brussels, Jul. 7-12, 1991, preprints vol. "engineering" pages 81-88) and, like them, likewise require for their design information on upper limits of the model uncertainties, parameter fluctuations, disturbances and frequencies. No compensation of linear or nonlinear components is performed. Control is performed exclusively by fuzzy rules which are derived heuristically from the phase plane. A disadvantage of these controllers is their limitation to pure fuzzy rules without taking account of easily implementable compensation components and without including additional filters such as, for example, a boundary layer. Furthermore, most fuzzy controllers are limited to processing an error and the timed derivative thereof in second-order systems (K. L. Tang, R. J. Mulholland: Comparing Fuzzy Logic with Classical Controller Designs; IEEE Trans. on Syst., Man and Cybernetics, Vol. SMC-17, No. 6, November/December 1987, pages 1085-1087). In the case of such fuzzy controllers, increasing the order leads to an exponentially growing increase in the number of rules. A further disadvantage of these controllers is that, as in the case of sliding-mode controllers without a boundary layer, a discontinuous change in sign (chattering) of the manipulated variable cam take place at the edges of the normalized phase plane,i and this leads to an undesired loading of the actuators. In addition, fuzzy controllers, whose membership functions are not tuned finely enough in the vicinity of the sliding surface, tend to undesired limit cycles.
It is the object of the invention to specify a controller for dynamic nth-order systems which combines the advantages of the sliding-mode controller with boundary layer and those of the fuzzy controller, that is to say a robust controller for a wide class of nonlinear nth-order systems which, operating on the basis of fuzzy rules on the one hand and of conventional, crisp control on the other hand, combines the advantages of the two technologies.